Image forming apparatus including position detector

ABSTRACT

An image forming apparatus includes a movable member that moves cyclically in synchronization with an image forming process and a position detector. The position detector includes a scale, an image sensor, a signal processor, and a position computing unit. The scale is attached to the movable member and includes a plurality of optical marks formed in line at a substantially constant interval. The image sensor captures data relating to at least one optical mark at a time. The signal processor computes a coordinate of the optical mark with respect to a reference position. The position computing unit computes a distance traveled by the optical mark based on a number of the optical marks that pass the reference position and the coordinate of the optical mark with respect to the reference position.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention generally relates to an image forming apparatus,and more particularly to an image forming apparatus including a positiondetector capable of detecting a relative position of and the distancetraveled by a movable component and/or a rotational component.

2. Discussion of the Background

In general, image forming apparatuses that employ electrophotographicprinting methods, such as copying machines, printers, facsimilemachines, etc., include an image forming mechanism and movable elements,such as a photoconductor drum, a transfer belt, and/or a conveyancemember. For example, in one electrophotographic printing method, theimage forming mechanism forms an electrostatic latent image on arotating photoconductor drum, develops it with toner, and transfers thedeveloped image onto a recording sheet. The recording sheet is conveyedto the image forming mechanism by a conveyance belt.

A color image may be formed by superimposing images of different colorson top of one another. Images of different colors on a recording sheetor a transfer member may be displaced relative to each other when beingsuperimposed, which blurs the color image. Therefore, positioning of theimages is important to avoid position displacement among the differentcolors of a color image. Positioning may require detection of position,distance traveled, and/or speed of a movable element.

One type of image forming apparatus includes an image sensor to measurepositional displacement. The image sensor reads an image on a movablepart, compares the current image data with a previously read image data,and computes the position of the image. The above method is convenientsince it requires only a detector and a reference scale is not required.However, extensive calculations may be required to accurately calculatethe position or distance traveled by the image using only an imagesensor.

One type of position detector may employ a method in which a correlationcoefficient of density data of an optical mark is calculated and aposition having a highest correlation is regarded as a relativedisplacement position. A large amount of calculation may be requiredbecause a correlative coefficient regarding every pixel is calculated.

Another type of image forming apparatus is provided with an encoderincluding a scale having a pattern in which optical marks are arrangedat substantially constant intervals to detect and to measure thedistance traveled by a movable element. The encoder detects positionand/or speed of the movable element, measures them using the scale, andconverts the measured values into electrical signals. However, toaccurately calculate a relative position or distance traveled by amovable element, a highly accurate optical system and high quality scaleand sensor are required. Furthermore, when optical marks are provided ona flexible or deformable component, variation may be caused in theintervals due to environmental factors, such as temperature and/orhumidity.

SUMMARY OF THE INVENTION

Various embodiments disclosed herein describe an image forming apparatusthat includes a position detector that may detect a relative position ofa movable member. In one example embodiment, an image forming apparatusincludes a position detector and a movable member that cyclically movesin synchronization with an image forming process. The position detectorincludes a scale, an image sensor, a signal processor, and a positioncomputing unit. The scale is attached to the movable member and includesa plurality of optical marks formed in line at a substantially constantinterval. The image sensor detects the scale at a constant cycle andreads at least one optical mark at a time. The signal processor computesa coordinate of the optical mark read by the image sensor from areference position provided to the scale image. The position computingunit computes an absolute travel distance of the optical mark based onthe coordinate of the optical mark and a number of the optical marksthat pass the reference position.

Another embodiment includes a position detector which may detect arelative position of a movable member. The position detector includes ascale, an image sensor, a signal processor, and a position computingunit. The scale is attached to the movable member and includes aplurality of optical marks formed in line at a substantially constantinterval. The image sensor detects the scale at a constant cycle andreads at least one optical mark at a time. The signal processor computesa coordinate of the optical mark read by the image sensor from areference position provided to the scale. The position computing unitcomputes an absolute travel distance of the optical mark based on anumber of the optical marks that pass the reference position and thecoordinate of the optical mark.

Yet another embodiment includes a travel detector which may detect arotation speed and a position of a rotationally movable member. A traveldetector unit includes a scale, an image sensor, a signal processor, anda position computing unit. The scale is attached to the rotationallymovable member and includes a plurality of optical marks formed in lineat a substantially constant interval. The image sensor detects the scaleimage at a constant cycle and reads at least one optical mark at a time.The signal processor computes a coordinate of the optical mark read bythe image sensor from a reference position provided to the scale image.The position computing unit computes an absolute travel distance of theoptical mark based on a number of the optical marks that pass thereference position and the coordinate of the optical mark.

BRIEF DESCRIPTION OF THE DRAWINGS

A more complete appreciation of the disclosure and many of the attendantadvantages thereof will be readily obtained as the same becomes betterunderstood by reference to the following detailed description whenconsidered in connection with the accompanying drawings, wherein:

FIG. 1 is an illustration of an image forming apparatus according to anembodiment of the present invention;

FIG. 2 is an illustration of a belt conveyance unit in which a relativeposition detector of FIG. 1 is applied;

FIG. 3 is a schematic diagram illustrating the relative positiondetector of FIG. 2;

FIG. 4 is a block diagram of the relative position detector of FIG. 3;

FIG. 5 is an illustration of example images on a light receiving surfaceof an image sensor of FIG. 4;

FIG. 6 is an illustration of examples of position measurement data bythe image sensor of FIG. 4;

FIG. 7 is an illustration of an example of position measurement data bythe image sensor of FIG. 4;

FIG. 8 is an illustration of a relative position detector according toan embodiment of the present invention;

FIG. 9 is an illustration of examples of position measurement data byimage sensors of FIG. 8; and

FIG. 10 is an illustration of a relative position detector according toan embodiment of the present invention.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

In describing preferred embodiments illustrated in the drawings,specific terminology is employed for the sake of clarity. However, thedisclosure of this patent specification is not intended to be limited tothe specific terminology so selected and it is to be understood thateach specific element includes all technical equivalents that operate ina similar manner. Referring now to the drawings, wherein like referencenumerals designate identical or corresponding parts throughout theseveral views, particularly to FIG. 1, an image forming apparatus 100according to an embodiment of the present invention is described.

The image forming apparatus 100 is a tandem image forming apparatus, andincludes four individual image forming units. As illustrated in FIG. 1,the image forming apparatus 100 includes a relative position detector10, a scale 11, a conveyance belt 20, and image forming units 51K, 51M,51Y, and 51C for forming black, magenta, yellow, and cyan images,respectively. The image forming apparatus 100 further includes a paperfeeding tray 52, a fixing unit 53, a driving roller 54, and a drivenroller 55. The paper feeding tray 52 contains a sheet 56, such as one ormore sheets of paper.

The image forming unit 51K includes a photoconductive drum 57K and acharging unit 58K, an exposure unit 59K, a development unit 60K, atransfer unit 61K, and a cleaner 63K located around the photoconductivedrum 57K. The exposure unit 59K emits an exposure light 62K. Each of theother image forming units 51M, 51Y, and 51C has a similar configurationand a similar function to the image forming unit 51K. The relativeposition detector 10 may detect a relative position and speed of theconveyance belt 20. The scale 11 includes a plurality of optical marksformed at substantially constant intervals, and is attached to theconveyance belt 20. The relative position detector 10 senses that theoptical mark is moving, and detects the relative position and speed ofthe conveyance belt 20. The relative position detector 10 and scale 11are described in further detail below. The conveyance belt 20 is anendless belt, and is stretched between the driving roller 54 and drivenroller 55. The driving roller 54 is driven to rotate, and drives thedriven roller 55. The driving roller 54 causes the conveyance belt 20 torotate in the direction of arrow C in synchronization with an imageforming process.

The image forming units 51K, 51M, 51Y, and 51C are arranged in orderalong the conveyance belt 20. The top sheet 56 in the paper feeding tray52 located below the conveyance belt 20 is sent to the conveyance belt20 and adheres to an outer surface of the conveyance belt 20 byelectrostatic adsorption. The sheet 56 is first sent to the imageforming unit 51K provided at the uppermost stream in the movingdirection of the conveyance belt 20.

In the image forming unit 51K, the charging unit 58K uniformly charges acircumference surface of the photoconductive drum 57K in a darkcondition. In one example, the exposure unit 59K may be a laser scanner.In the exposure unit 59K, a laser beam from a laser source is reflectedby a polygon mirror. The reflected laser light is then emitted as anexposure light 62K via an optical system employing an f-theta lens, adeflective mirror, and the like to form an electrostatic latent image onthe photoconductive drum 57K. The developing unit 60K develops theelectrostatic latent image on the photoconductive drum 57K into avisible black image using black toner. The transfer unit 61K transfersthe black image onto the sheet 56 at a position where thephotoconductive drum 57K is in contact with the sheet 56 on theconveyance belt 20. The cleaner 63K removes any remaining toner left onthe photoconductive drum 57K after the black image is transferred to thesheet 56.

The sheet 56 on which the black image is formed is next sent to imageforming unit 51M, in which a magenta image is superimposed on the blackimage in a process similar to that performed in image forming unit 51K.The sheet 56 is then sent to image forming unit 56Y, in which a yellowimage is superimposed on the black and magenta images in a processsimilar to that performed in image forming unit 51K. The sheet 56 isthen sent to image forming unit 56C, in which a cyan image issuperimposed on the black, magenta, and yellow images on the sheet 56 ina process similar to that performed in image forming unit 51K to obtaina full color image on the sheet 56.

The sheet 56 on which the full color image is formed is removed from theconveyance belt 20 after passing through the image forming unit 51C.Next, the fixing unit 53 fixes the full color image on the sheet 56.

A belt conveyance unit 200 including the relative position detector 10is described below with reference to FIG. 2.

As illustrated in FIG. 2, a belt conveyance unit 200 includes aconveyance belt 20 a, a controller 30, a motor driver 31, a motor 32,and a driving roller 54. The belt conveyance unit 200 also includes arelative position detector 10 having a scale 11, an image sensor 14, asignal processor 15, and a position computing unit 16. A plurality ofoptical marks 12 are formed in the scale 11 at substantially constantintervals (pitch).

The conveyance belt 20 a may be an endless belt stretched tightly aroundthe driving roller 54. The driving roller 54 is driven by the motor 32,rotates and causes the conveyance belt 20 a to move in the directionshown by arrow B. The controller 30 controls the motor driver 31. Thescale 11 having the plurality of optical marks 12 is provided at apredetermined position on conveyance belt 20 a, such as an edge of theconveyance belt 20 a, so that the scale 11 encircles a periphery surfaceof the conveyance belt 20 a. The optical marks 12 may display apredetermined reflectance or transmittance that is different from thatof a base material of the scale 11 and/or the conveyance belt 20 a.

The position detector 10 detects a relative position of the scale 11attached to the movable conveyance belt 20 a. A plurality of imagingelements, or pixels, arranged in the image sensor 14 may read an imageof the scale 11 by capturing data relating to the scale 11 at constantcycles and converting the image to an electric signal. The signalprocessor 15 converts the image data obtained by the image sensor 14into position measurement data. Based on the position measurement data,the position computing unit 16 computes a relative position of the scale11. Using the relative position of the scale 11, a relative positionand/or speed of the movable conveyance belt 20 a may be obtained, andthe controller 31 may control the motor driver 31 to adjust the movementof the conveyance belt 20 a.

A CPU (central processor) or a DSP (digital signal processing) may beused as the controller 30. A common CPU or DSP may be used as thecontroller 30 and position computing unit 16 to simplify theconfiguration of the belt conveyance unit 200 if the positioncomputation is executed programmatically.

The relative position detector 10 according to various embodiments isdescribed below in detail with reference to FIGS. 3 and 4.

FIG. 3 illustrates a schematic configuration of the relative positiondetector 10, and FIG. 4 is block diagram of the relative positiondetector 10. The relative position detector 10 further includes a lightsource 13 to irradiate the scale 11, as illustrated in FIG. 3, and animaging lens through which an image of the optical mark 12 is imaged ona light receiving surface of the image sensor 14, as illustrated in FIG.4.

As illustrated in FIG. 4, the signal processor 15 includes an analog todigital conversion circuit (A/D conversion circuit) 15-1, a filter 15-2,and a center extraction circuit 15-3. The position computing unit 16includes a mark counter 16-1, a position computing circuit 16-2, and acumulative position computing unit 16-3.

The optical marks 12 have a reflectance or transmittance that differfrom the reflectance or transmittance of a base material of the scale 11and/or the conveyance belt 20 a. The optical marks 12 may be arranged inany pattern that causes the amount of light received by the image sensor14 to fluctuate. The fluctuation of the amount of light received maycause a density difference on the image sensor 14, which is recognizableas the image. FIG. 3 illustrates a pattern of black lines on a whitebackground as an example of the optical marks 12. Other examples ofoptical marks 12 include a pattern of white lines on a black background,a transmissive pattern of metal slits, or the like.

In one embodiment, the relative position detector 10 detects themovement of the optical mark 12. Therefore, image sensor 14 isconfigured to be capable of reading at least one optical mark 12, andthe imaging lens 17 is configured to have a diameter capable of imagingat least one optical mark 12. The image sensor 14 reads the scale 11,which is moving in the direction of arrow B at constant cycles, byforming an image of the optical mark 12 in the scale 11 on the lightreceiving surface of the image sensor 14 through the imaging lens 17.Light receiving efficiency of the image sensor 14 may be improved byirradiating the scale 11 with the light source 13. As a result, theelectric signal obtained by the image sensor may have an improved signalto noise (S/N) ratio.

Devices such as a charge-coupled device (CCD) or a complementary metaloxide semiconductor (CMOS) sensor may be used as the image sensor 14. Anarray of the imaging elements (pixels) may be a one-dimensional array(one-dimensional sensor) or a two-dimensional array (two-dimensionalsensor).

The A/D conversion circuit 15-1 converts data obtained by the imagesensor 14 into digital data by converting the image to density dataaccording to the amount of light received by the image sensor 14. Thefilter 15-2 filters out noise in the data. The center extraction circuit15-3 extracts center positions of the respective optical marks 12 fromthe density data (optical mark center data).

The mark counter 16-1 keeps track of the number of optical marks 12 thatpass a reference position. The reference position may be a coordinate ofa position on the light receiving surface of the image sensor 14, or aline on the light receiving surface of the image sensor 14 in a movingdirection of the optical marks 12. The X-coordinate and Y-coordinate ofthe reference position are set to zero, respectively (X=0, Y=0). Theposition computing circuit 16-2 computes displacement (distance) of theoptical mark 12 from the reference position. The cumulative positioncomputing unit 16-3 computes a current position of the optical mark 12based on the count of the mark counter 16-1 and the position (i.e.coordinates) of the optical mark 12 on the image sensor 14.

By using an image sensor in combination with a scale, the relativeposition detector 10 may provide high accuracy, stability, and highresolution in measuring a relative position of a movable and/or rotatingcomponent.

Functions of the signal processor 15 and position computing unit 16, anddata processing is explained below with reference to FIG. 5. FIG. 5illustrates example images 1, 2, and 3 on the light receiving surface ofthe image sensor 14. The example images 1, 2, and 3 include opticalmarks 12 and a reference position 12-1, respectively. Example image 1 isthe image before A/D conversion, example image 2 is the density dataafter A/D conversion, and example image 3 is optical mark center data.The optical marks 12 are arranged in the direction of arrow D on thelight receiving surface. In FIG. 5, two linear optical marks 12 areimaged.

As described above, the signal processor 15 converts the image dataobtained by the image sensor 14 into position measurement data. If theimage sensor 14 is a CCD, an analog signal synchronized with a clock isoutput. The image sensor 14 reads the image of the scale 11 at cyclescorresponding to a required or desired resolution.

The A/D conversion circuit 15-1 converts the analog signal into adigital signal. If the image sensor 14 is a CMOS sensor, the image datamay be read out by designating an address of the pixel and the data maybe extracted by scanning the data. Thus, the data of the densitydifference according to the amount of light received by the image sensor14 (density data) may be obtained as illustrated in image 2.

The mark center extraction circuit 15-3 extracts the center positions ofthe respective optical marks 12, generates the optical mark center dataof the optical marks 12 as illustrated in image 3, and sends the opticalmark center data to the position computing unit 16. The center positionsof the optical marks 12 may be derived using methods such as a method inwhich a threshold level is set to determine the center of an up edge anda down edge, a method in which a center of gravity is figured out, orthe like.

The position computing unit 16 receives the optical mark center data,which locates the position of the optical mark 12 on the image sensor14, and converts the optical mark center data to relative position dataon the scale 11, which locates a relative position of the optical mark12 in real space of the image sensor 14 and the scale 11.

According to an embodiment described above, the mark counter 16-1 countswhen the optical mark 12 read by the image sensor 14 passes thereference position 12-1, that is, the number of optical marks 12 thatpass the reference position 12-1. Absolute distance traveled by thescale 11 may be calculated using the formula:X=P·N+d

in which X is the absolute travel distance of the scale 11, N is thecount by the mark counter 16-1, P is the pitch between the optical marks12, and d is the distance from the reference position 12-1 to theoptical mark 12 that is a nearest optical mark to the reference position12-1 in the moving direction of the scale 11.

FIG. 6 illustrates examples of position measurement data R1, R2, and R3.Each of R1, R2, and R3 is accompanied by an example of a calculation ofdistance traveled by the optical mark 12 according to the above formula.In FIG. 6, a pitch P0 of optical marks 12, and optical mark centers M1,M2, and M3 are illustrated. The optical marks 12 move in the directionof arrow D. Distance between the reference position 12-1 and opticalmark center M1 or M2 on the image sensor 14 is shown as d1, d2, or d3.

The measurement data R1 is obtained after the optical mark center M1passes the reference position 12-1 and travels the distance d1.Therefore, the travel distance X in the measurement data R1 is P0·1+d1.Likewise, the travel distance X in the measurement data R2 is P0·1+d2.The measurement data R3 is obtained after two optical mark centers M1and M2 pass the reference position 12-1 and travel the distance d3.Therefore, the travel distance X in the measurement data R3 is P0·2+d3.

In an embodiment described above, the optical mark center position datamay be generated from density data according to the amount of lightreceived by the image sensor, and travel distance of the scale may becalculated by computing the center position of the optical mark. Thecumulative travel distance of the scale 11 may be calculated by usingthe number of optical marks 12 that pass a reference position on theimage sensor and the current distance d of the optical mark 12 from thereference position, instead of accumulating the travel distance of theoptical mark. Therefore, position detection may be performed accordingto the accuracy of the optical mark. The functions described above maybe achieved by using software or a gate array, which is described below.

It is difficult to provide optical marks at accurate intervals on aflexible component, for example, on an intermediate transfer belt.Further, if the flexible component is deformable due to temperatureand/or humidity optical marks on the flexible component may be placed aterroneous intervals.

Therefore, an image sensor according to an embodiment is configured tobe capable of detecting at least two optical marks in a scale at a time.The detected optical marks are imaged on the image sensor, and aninterval (pitch) of the optical marks is computed based on the images onthe image sensor. Based on the computed interval of the optical marks,the distance traveled by the scale may be corrected.

To detect at least two optical marks 12 as described above, the imagesensor 14 is configured to be larger than the width of two optical marks12 and the distance between them (pitch). When the pitch of the opticalmark 12 is P and the width of the optical mark 12 is o, the size of theimage sensor 14, S, is expressed as follows.S>P+o·2.

In FIG. 7, the optical center positions M1 and M2 of optical marks 12and the pitch P(1) are illustrated. When optical marks are not arrangedat an accurate pitch on a scale, or highly accurate measurement isrequired, a position of the optical mark 12 may be calculated by usingthe following formula:

$x = {{\sum\limits_{k = 1}^{n}\;( {P(k)} )} + x}$

where X is the position of the optical mark 12, x is the distance of theoptical mark center M1 from the reference position 12-1, Σ representssummation of a set of natural numbers from 1 to n, k is an arbitrarynumber in the set, and n is a largest number in the set.

Therefore, highly accurate cumulative position measurement may beperformed because a value of the pitch of the optical marks is correctedduring the computation of distance traveled.

FIG. 8 illustrates a relative position detector 10 a according to anembodiment of the present invention. In FIG. 8, the relative positiondetector 10 a includes a scale 11, a plurality of optical marks 12,image sensors 14-1 and 14-2, and imaging lenses 17-1 and 17-2. The scale11 moves in the direction of arrow D. The image sensors 14-1 and 14-2are provided at an interval g. A plurality of image sensors 14-1 and14-2 are provided along the traveling direction of the scale 11. Theinterval g is expressed as g=N·P0, wherein N is the count by the markcounter 16-1 and P0 is the pitch of optical marks 12. An image of thescale 11 is imaged on the image sensor 14-1 through the imaging lens17-1. Likewise, an image of the scale 11 is imaged on the image sensor14-2 through the imaging lens 17-2.

FIG. 9 illustrates position measurement data R4 and R5. The positionmeasurement data R4 is data of the optical marks 12 obtained by imagesensors 14-1, and position measurement data R5 is data of the opticalmark 12 obtained by the image sensor 14-2. In the position measurementdata R4 and R5, reference positions 12-1 and optical mark centers M3 andM4 are included. An error in the pitch P0 is expressed as xa−xb, wheredistance between M3 and the reference position 12-1 on the image sensor14-1 is xa and distance between M4 and the reference position 12-1 onthe image sensor 14-2 is xb. The image sensors 14-1 and 14-2 are placedat interval g, as above. Based on the error xa-xb, a new pitch P′ may becalculated by using a following formula.P′=P0+(xa−xb)/N

Therefore, the pitch used in the calculation of the travel distance ofthe scale 11 may be corrected to the new pitch P′. In other respects,the relative position detector 10 a may have a similar configuration andfunction to the relative position detector 10 illustrated in FIG. 4.

When the image sensors 14-1 and 14-2 are provided at a distance in whichthe optical marks 12 are counted N times as described above, the errorin the pitch of the optical marks 12 is magnified N times. That is,pitch of optical marks may be corrected accurately by providing imagesensors spaced a distance from each other, which magnify errors in thepitch of the optical marks.

FIG. 10 illustrates a relative position detector 10 b according to anembodiment of the present invention. In FIG. 10, the relative positiondetector 10 b includes a scale 11, a plurality of optical marks 12, animage sensor 14, imaging lenses 17-1, and 17-2, and mirrors 18, 19-1,and 19-2. The scale 11 is moving in the direction of arrow D. Theimaging lenses 17-1 and 17-2, and the mirrors 18, 19-1, and 19-2function as an integrated optical system. This relative positiondetector 10 b is an example in which different portions of the scale 11are imaged on the single image sensor 14 through the integrated opticalsystem. In other respects, the relative position detector 10 b may havea similar configuration and function to the relative position detector10 a of FIG. 8.

The single image sensor 14 may process images and compute centerpositions of the optical marks 12 because the relative position detector10 b is capable of imaging different portions of the scale 11 on asingle image sensor 14. Therefore, efficiency may be improved and costmay be reduced. Further, the pitch of the optical marks 12 may beaccurately corrected, because the different portions of the scale 11 aremeasured to correct the pitch.

Although an integrated optical system including mirrors is described inthe above embodiment, alternatively, an optical system using imagetransfer by image fibers and/or a refracting optical system using aprism may be applied to the image sensor. Further, a two-dimensionalimage sensor may be used. In such a case, two-dimensional displacementmeasurement may be performed by using a scale arranged in twodimensions. Further, a photodiode array may be used instead of an imagesensor.

As described above, according to various embodiments of the presentinvention, the distance traveled by a movable component on which a scaleis provided may be measured while correcting the pitch of optical markson a belt-like component that may be deformed due to environmentalinfluence.

The relative position detector according to the various embodiments maybe used to detect the position of a component. For example, the relativeposition detector may detect a relative position and/or speed of arotationally movable component, such as a photoconductor drum, despitethe fact that it is difficult to approximate an encoder head to arotating component having a cylindrical surface because the height of aportion to be detected changes. Therefore, the speed of such arotationally movable component may be stabilized, and a highly accurateimage may be formed.

Numerous additional modifications and variations are possible in lightof the above teachings. It is therefore to be understood that within thescope of the appended claims, the disclosure of this patentspecification may be practiced otherwise than as specifically describedherein.

This patent specification claims priority under 35 U.S.C. §119 toJapanese patent applications, No. JP-2005-301128 filed on Oct. 17, 2005and No. JP-2006-252385 filed on Sep. 19, 2006 in the Japan PatentOffice, the entire contents of which are incorporated by referenceherein.

1. An image forming apparatus, comprising: an electrophotographic imageforming element configured to move cyclically and to convey toner to arecording sheet; a movable member configured to move cyclically insynchronization with the electrophotographic image forming element andto convey the recording sheet to the electrophotographic image formingelement; and a position detector comprising: a scale attached to themovable member and including a plurality of optical marks formed in lineat a substantially constant interval, an image sensor configured tocapture an image of at least two of the plurality of optical marks andthe interval between the at least two optical marks at a time, the imagesensor further configured to be larger than the width of two of theplurality of optical marks and the interval between the two opticalmarks, a signal processor configured to determine a coordinate of anoptical mark with respect to a reference position using the datacaptured by the image sensor, and a position computing unit configuredto compute a distance traveled by at least one of the optical marksbased on a number of the optical marks that pass the reference positionand the coordinate of the at least one optical mark with respect to thereference position and to determine the value of the interval betweenthe at least two optical marks based on the image of the at least twooptical marks.
 2. The image forming apparatus according to claim 1,wherein the plurality of optical marks have a predetermined differencein reflectance or transmittance from a base material of the scale. 3.The image forming apparatus according to claim 1, wherein the positioncomputing unit is further configured to correct the distance traveled bythe at least one optical mark based on the determined value of theinterval between the at least two optical marks.
 4. The image formingapparatus according to claim 1, wherein the image sensor is atwo-dimensional image sensor, and the plurality of optical marks arearranged in two dimensions in the scale.
 5. A position detector,comprising: a scale attached to a movable member and including aplurality of optical marks formed in line at a substantially constantinterval; an image sensor configured to capture an image of at least twoof the plurality of optical marks and the interval between the at leasttwo optical marks at a time, the image sensor further configured to belarger than the width of two of the plurality of optical marks and theinterval between the two optical marks; a signal processor configured todetermine a coordinate of an optical mark with respect to a referenceposition using the data captured by the image sensor; and a positioncomputing unit configured to compute a distance traveled by the opticalmark based on a number of the optical marks that pass the referenceposition and the coordinate of the optical mark with respect to thereference position and to determine the value of the interval betweenthe at least two optical marks based on the image of the at least twooptical marks.
 6. A travel detector for detecting a rotation speed and aposition of a rotationally movable member, comprising: a scale attachedto a rotationally movable member and including a plurality of opticalmarks formed in line at a substantially constant interval; an imagesensor configured to capture an image of at least two of the pluralityof optical marks and an interval between the two optical marks at atime, the image sensor further configured to be larger than the width oftwo of the plurality of optical marks and the interval between the twooptical marks; a signal processor configured to determine a coordinateof an optical mark with respect to a reference position using the datacaptured by the image sensor; and a position computing unit configuredto compute a distance traveled by the optical mark based on a number ofthe optical marks that pass the reference position and the coordinate ofthe optical mark with respect to the reference position and to determinethe value of the interval between the at least two optical marks basedon the image of the at least two optical marks.